n^2-10n-20=0

Solution for n^2-10n-20=0 equation:

n^2-10n-20=0

a = 1; b = -10; c = -20;
Δ = b2-4ac
Δ = -102-4·1·(-20)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*1}=\frac{10-6\sqrt{5}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*1}=\frac{10+6\sqrt{5}}{2}
$